Nonlinear states and dynamics in a synthetic frequency dimension

Abstract

Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori low-dimensional systems. However, the influence of nonlinear effects on the synthetic frequency dimensions was studied only under significant restrictions. In the present paper, we develop a generalized mean-field model for the optical field envelope inside a single driven-dissipative resonator with quadratic and cubic nonlinearities, whose frequencies are coupled via an electro-optical resonant temporal modulation. The leading order equation takes the form of driven Gross-Pitaevskii equation with a cosine potential. We numerically investigate the nonlinear dynamics in such microring resonator with a synthetic frequency dimension in the regime where parametric frequency conversion occurs. In the case of anomalous dispersion, we find that the presence of electro-optical mode coupling confines and stabilizes the chaotic modulation instability region. This leads to the appearance of a novel type of stable coherent structures which emerge in the synthetic space with restored translational symmetry, in a region of parameters where conventionally only chaotic modulation instability states exist. This structure appears in the center of the synthetic band and, therefore, is referred to as Band Soliton. Finally, we extend our results to the case of multiple modulation frequencies with controllable relative phases creating synthetic lattices with nontrivial geometry. We show that an asymmetric synthetic band leads to the coexistence of chaotic and coherent states of the electromagnetic field inside the cavity i.e. dynamics that can be interpreted as chimera-like states. Recently developed ${\chi }^{(2)}$ microresonators can open the way to experimentally explore our findings.

arXiv comment12 pages, 5 figures; figure 4 and typos corrected

References in corpus (37)

• Topological Photonics
• Topological Photonics
• Temporal solitons in optical microresonators
• Broadband electro-optic frequency comb generation in an integrated microring resonator
• Mode interaction aided excitation of dark solitons in microresonators constructed of normal dispersion waveguides
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Nonlinear topological photonics
• Synthetic Dimension in Photonics
• Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
• Stability Analysis of the Lugiato-Lefever Model for Kerr Optical Frequency Combs. Part I: Case of Normal Dispersion
• Soliton crystals in Kerr resonators
• Topological quantum matter in synthetic dimensions
• Photonic Topological Insulator in Synthetic Dimensions
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Integrated gallium phosphide nonlinear photonics
• Quantum simulation of an extra dimension
• A single photonic cavity with two independent physical synthetic dimensions
• Dynamics of soliton crystals in optical microresonators
• Photonic gauge potential in a system with a synthetic frequency dimension
• Frequency combs and platicons in optical microresonators with normal GVD
• Turn-key, high-efficiency Kerr comb source
• Photon propagation in a discrete fiber network: An interplay of coherence and losses
• Experimental band structure spectroscopy along a synthetic dimension
• Integrable turbulence and formation of rogue waves
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• From the Lugiato-Lefever equation to microresonator based soliton Kerr frequency combs
• Higher-order topological insulators in synthetic dimensions
• Frequency comb formation in doubly resonant second-harmonic generation
• Chirality of topological gap solitons in bosonic dimer chains
• Statistical properties of nonlinear stage of modulation instability in fiber optics
• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions
• Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
• Turbulence-induced rogue waves in Kerr resonators
• Nonlinear solutions for χ^(2) frequency combs in optical microresonators
• Temporal quadratic solitons and their interaction with dispersive waves in Lithium Niobate nano-waveguides
• Two-color flat-top solitonic pulses in ${\chi }^{(2)}$ optical microresonators via second harmonic generation
• Modeling of quasi-phase-matched cavity enhanced second harmonic generation

Cited by in corpus (18)

• Integrated photonics on thin-film lithium niobate
• High-efficiency and broadband electro-optic frequency combs enabled by coupled micro-resonators
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices
• A comprehensive review on developments of synthetic dimensions
• Piezoelectric actuation for integrated photonics
• Scaling optical computing in synthetic frequency dimension using integrated cavity acousto-optics
• Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point
• Dissipative Kerr solitons, breathers and chimera states in coherently driven passive cavities with parabolic potential
• Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization
• Simulating topological materials with photonic synthetic dimensions in cavities
• Synthetic non-Abelian Electric Fields and Spin-Orbit Coupling in Photonic Synthetic Dimensions
• On measuring the Hubble constant with X-ray reverberation mapping of active galactic nuclei
• On-chip multi-timescale spatiotemporal optical synchronization
• Mean-field equation for phase-modulated optical parametric oscillator
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Spectral shaping of fast-gain frequency combs through phases in synthetic dimensions
• Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities